Erasure-Biased Noise from Angular Momentum Diffusion: An OAM Analog of Cat-Qubit Protection (v2)

Abstract

Bosonic "cat qubits" encoded in superpositions of well-separated coherent states |+a⟩ and |-a⟩ are attractive for quantum error correction because single-photon loss acts as a phase-flip error while the dominant, hardware-limiting bit-flip error is suppressed exponentially in the mean photon number |a|². We ask whether an analogous noise bias can be engineered using the orbital angular momentum (OAM) of light instead of its amplitude, encoding a qubit in a superposition of two well-separated OAM eigenstates |+L⟩ and |-L⟩. We model the dominant OAM channel noise—local mode-mixing induced by fiber imperfections or wavefront aberrations, which couples only adjacent topological charges (Δl = ±1)—as a continuous-time random walk on the integers. We define an operational experimental protocol to extract the channel hopping rate directly from the linear spatial growth of the OAM variance Var(l) = γz. We show analytically and numerically that this local, nearest-neighbor character converts almost all population leakage out of the code space into a detectable erasure, while the probability of an undetected logical bit-flip is suppressed as exp(-2L² / γz), a direct structural analog of the exp(-2|a|²) bias of amplitude-phase cat qubits. This revised version (v2) corrects the erasure-probability expression using an exact closed form (Skellam/Bessel identity), adds an explicit resource-overhead analysis quantifying the repetition cost of the scheme, and discusses the impact of a mode-dependent hopping rate γ(l) on the achievable suppression. We argue that periodic syndrome extraction using existing phase-locked OAM mode sorters could realize the required error-detection step without a dedicated nonlinear dissipative stabilizer. ---Keywords: Quantum Error Correction, Cat Qubits, Orbital Angular Momentum (OAM), Noise Bias, Erasure Channel, Random Walk, Frugal Quantum Hardware, Open Science.Repository contents: Includes manuscript PDF and full Python simulation package (NumPy/SciPy/Matplotlib).